Finite Group Databasebeta

← #13069886

Subgroups — #13069886

Order 1408.

274 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
2#10622850C211yesmaximal, characteristic, complemented
3#10622849C211yesmaximal, characteristic, complemented
4C2×#66897C211yesmaximal, characteristic, complemented
5#10622828C211yesmaximal, characteristic, complemented
6#10622737C211yesmaximal, characteristic, complemented
7#10622197C211yesmaximal, characteristic, complemented
8C2×C11×#41C2211yescharacteristic
9C22×D4×C11C2211yescharacteristic
10C11×AGL(1,ℤ/8)—22no—
11C11×AGL(1,ℤ/8)—22no—
12C2×C11×SD16—21no—
13C2×C11×D8—21no—
14C2×C11×M16C2211yescharacteristic
15#66979C2211yescharacteristic
16C2×#4318C2211yescharacteristic
17C2×#4318C2211yescharacteristic
18C2×#4318C2211yescharacteristic
19#66901—22no—
20#66900—21no—
21#66897—21no—
22#66897—22no—
23#66896—22no—
24#66886—22no—
25C24×C11—21no—
26C11×#41—21no—
27C11×#41—21no—
28C11×#41—21no—
29C11×#41—21no—
30C2×Q8×C11D411yescharacteristic
31C2×D4×C11—21no—
32C2×D4×C11—21no—
33C2×D4×C11—21no—
34C2×D4×C11—21no—
35C2×D4×C11—21no—
36C2×D4×C11—21no—
37C2×D4×C11D412yes—
38C2×D4×C11D411yescharacteristic
39C22×C4×C11—21no—
40C22×C4×C11C2311yescharacteristic
41C11×SD16—24no—
42C11×D8—24no—
43C11×M16—21no—
44C11×M16D412yes—
45C2×C8×C11—21no—
46C22⋊Dic11—21no—
47C4⋊Dic11—21no—
48C4×Dic11—21no—
49#4318—21no—
50#4318—21no—
51#4318—21no—
52#4318—21no—
53#4318—21no—
54#4318D412yes—
55C2×C11⋊C8—21no—
56C2×C11⋊C8—21no—
57C2×C11⋊C8—21no—
58#2048—111nomaximal, Sylow
59C23×C11—22no—
60C23×C11—21no—
61C23×C11—41no—
62C23×C11—41no—
63C23×C11—82no—
64C23×C11#4111yescharacteristic
65Q8×C11—21no—
66Q8×C11—21no—
67D4×C11—21no—
68D4×C11—22no—
69D4×C11—21no—
70D4×C11—22no—
71D4×C11—41no—
72D4×C11—41no—
73D4×C11—41no—
74D4×C11—41no—
75C2×C4×C11—21no—
76C2×C4×C11—41no—
77C2×C4×C11—41no—
78C2×C4×C11C2×D411yescharacteristic
79C2×C4×C11C2×D411yescharacteristic
80C2×C4×C11C2×D411yescharacteristic
81C2×C4×C11C2×D411yescharacteristic
82C2×C4×C11#4111yescharacteristic
83C2×C4×C11#4111yescharacteristic
84C2×Dic11—41no—
85C8×C11—22no—
86C11⋊C8—22no—
87C11⋊C8—41no—
88C11⋊C8—41no—
89C2×AGL(1,ℤ/8)D1111yescharacteristic
90#430—111no—
91#421—111no—
92#418—111no—
93#413—111no—
94C2×#100—111no—
95#344—111no—
96C22×C11—41no—
97C22×C11—41no—
98C22×C11—42no—
99C22×C11—81no—
100C22×C11—82no—
101C22×C11—82no—
102C22×C11—82no—
103C22×C11#12111yescharacteristic
104C22×C11#12311yescharacteristic
105C22×C11#12411yescharacteristic
106C4×C11—41no—
107C4×C11#12011yescharacteristic
108C4×C11#12111yescharacteristic
109C4×C11#12111yescharacteristic
110C4×C11#12311yescharacteristic
111Dic11—81no—
112C2×#41C2×D1111yescharacteristic
113C22×D4C2×D1111yescharacteristic
114AGL(1,ℤ/8)—22no—
115AGL(1,ℤ/8)—22no—
116C2×SD16—21no—
117C2×D8—21no—
118C2×M16—111no—
119C2×M16—111no—
120C2×M16—111no—
121C2×M16C2×D1111yescharacteristic
122#117—111no—
123#108—222no—
124#104—222no—
125#102—222no—
126#101—221no—
127#100—222no—
128#100—221no—
129C2×C11—21no—
130C2×C11—21no—
131C2×C11—21no—
132C2×C11—81no—
133C2×C11—82no—
134C2×C11#39411yescharacteristic
135C24—21no—
136#41—21no—
137#41—21no—
138#41—21no—
139#41—21no—
140C2×Q8C22⋊D1111yescharacteristic
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4C22⋊D1111yescharacteristic
148C2×D4C22⋊D1112yes—
149C22×C4—21no—
150C22×C4C22×D1111yescharacteristic
151SD16—24no—
152D8—24no—
153M16—21no—
154M16—112no—
155M16—221no—
156M16—221no—
157M16—221no—
158M16—221no—
159M16—221no—
160M16C22⋊D1112yes—
161C2×C8—21no—
162C2×C8—221no—
163C2×C8—221no—
164C2×C8—221no—
165C4⋊C4—221no—
166C22⋊C4—221no—
167C42—221no—
168C11#204811yescharacteristic, complemented, Sylow
169C23—21no—
170C23—22no—
171C23—41no—
172C23—41no—
173C23—82no—
174C23#434111yescharacteristic
175Q8—21no—
176Q8—21no—
177D4—22no—
178D4—21no—
179D4—21no—
180D4—22no—
181D4—41no—
182D4—41no—
183D4—41no—
184D4—41no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—441no—
189C2×C4D4×D1111yescharacteristic
190C2×C4#434111yescharacteristic
191C2×C4#434111yescharacteristic
192C2×C4C2×C22⋊D1111yescharacteristic
193C2×C4C2×C22⋊D1111yescharacteristic
194C2×C4C2×C22⋊D1111yescharacteristic
195C8—22no—
196C8—222no—
197C8—441no—
198C8—441no—
199C22—41no—
200C22—41no—
201C22—42no—
202C22—82no—
203C22—81no—
204C22—82no—
205C22—82no—
206C22#6698811yescharacteristic
207C22#6698911yescharacteristic
208C22#6699211yescharacteristic
209C4—41no—
210C4—881no—
211C4#6698811yescharacteristic
212C4#6699111yescharacteristic
213C4#6699211yescharacteristic
214C4#6700611yescharacteristic
215C2—21no—
216C2—21no—
217C2—21no—
218C2—82no—
219C2—81no—
220C2#1062283511yescharacteristic
subgroupG/H
centerC2#10622835
commutator, cosocleC22×C4×C11C23
FrattiniC22×C4C22×D11
Fitting, prime radicalC2×C11×AGL(1,ℤ/8)C2
socleC2×C11#394
hypercenterC2×AGL(1,ℤ/8)D11
hypocenterC11#2048
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×AGL(1,ℤ/8)

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #10622850C2semidirect
3. #10622849C2semidirect
4. C2×#66897C2semidirect
5. #10622828C2semidirect
6. #10622737C2semidirect
7. #10622197C2semidirect
168. C11#2048semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C11×AGL(1,ℤ/8)2
#106228502
#106228492
C2×#668972
#106228282
#106227372
#106221972
#204811